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MAC2311 Test 2 (form A) Name: [(0 LL 0’71; Fall, 2011 Section (circlcyours) MWF 9:00 MWF 10:00 Calculator allowed. Unless otherwise directed, show work to earn partial credit. 1. When an object is projected vertically upward from the ground, its height in feet at time I seconds is given by SQ) = 641F461? feet for 0 S t S 4.
Average Velocity
(seconds ﬂee: er second
[m]
Liv£4 “3,2. V @10ch :: S , 00/
2: ﬁlﬁﬂjéﬁiﬂ : =~ 32 . ore . 00/
b) Find 12(3) , the instantaneous velocity at time i: 3 , by using the limit deﬁnition of derivative to a) Complete the table by calculating average velocity
over the time interval 3 S t 5 3.001. Do not round
off. .. record all digits shown by your calculator’s
default settings. calculate s’(3) Show all work to support your answer, and use appropriate units. 5a)? is ﬂew5(3) v(3):s’(3)='“32~ Ft’sec: lnezo Z
x m 3ft!iiéle:%l§;;52w:mi§m
To H2 MM w/éﬁjﬂwiﬁlwg
:2. {M wwwwwwmwr _. _
W0 h if” it?
' ’ m t” W" "' / A Yam’s Temperature (degrees Celsius) 30p 2. A cold Yam is placed in an oven preheated to 150°C . T
The graph shows the Yam’s temperature over a 3hour period. Sketch the tangent line to the graph at time I: 1 hour, and
estimate it’s slope. Then ﬁll in the blanks below to complete
conceptual interpret for this slope. Edi/{maiith (hug) “Mi (11‘733
tm  a: N  502, nitrate.“ aw wr“ ‘ w Conclusion: An hour after being in the oven the Yam’s temperature is increasing at an ‘I (15 inmihmﬂw rate of 50 oﬁ’ﬂr ( average 0! instantaneous ) ( numerical answerwithappmpriateunits ) 3. The piecewise—deﬁned f ~ graph shown is made from connecting a straight line segment and a quarter
circle. Sketch f’ . Be sure your sketch uses open/solid dots as needed. If the f’ graph is asymptotic,
use a dashed line to indicate the asymptote and label it with its equation. Graph of f Graph of f ' 1 3 4 5
ml m leak ‘i’Wmrcil iw (349 Keg?
H2 5+4xwx2 , x34 4. One piece of the graph of f ={ b 4
mx+ , x > is shown. Find values form and b that make
f differentiable at x = 4. Four” Kéllv) ﬁC’(x):ewa;x_ fézf)ﬁLl”Z(H)$mLi'  Ai‘" Tali; 51/0 We”, is, $0 Wig, \ﬁitt‘é‘féw
0w" m;+b in be. 2%)»: “trlo. y y moﬁ 6 7
m= we!“ : . = t W: ‘2 ,
_{_ I. p) ansmwg éga'ignm‘a ) we Naﬁi‘ 2/3,»: 93 ii) m w L} xai Pie Pdln'i” a all x + 2.! 5. The function f(_x) = 313)(x— 2)2 = 306—2); has domain (—00,+00). 3) Calculate f ’(x) and state its domain. ’% Z'H‘v—‘I I f'(x): '3: I I 7)
i c =_ 2:. —z e
i}: X) 3) 50‘ ) 1 domain of f’ ("’o"; 2") U(9‘I+m) \
I '73 2.
JZLK):'2(>('Z 1.: 3x ‘For‘ Xi; N 1)) Sketch enough of the f graph to Show its true
behavior at x = 2. The one—sided limits of f ’(x) as x—> 2‘ and x a}? may be useful 2— L 3? 31 i—xi E“:
Ki \3/ X'Z =1 no.9 0 = ' 00 . iinjia'hii’eiy 'Si‘m?
 .3 ‘ u .
2“ 6’03‘94'“ 6&5? if» Kriz
lm+ 3 1,; 5 #II . 751 1—};0 . . _5 .
D
39.2 \jK—l Pct‘ose 1‘0 0 6. Consider the table describing function j and the graph of function k. I.
6.
5.
4. Graph of k Let h(x)=j(x) m3): (ii/ﬁe ke)‘ I ,
Koo my} (*2: Hemmwwu iwnuﬁmmﬁe m3) ‘ﬁlﬁildﬂifigiil :2 fate :1 A 7. Choose either A. or B. but not both. Check the box for the problem you want graded. A. D The graph of f(x) =x+2cosx has an inﬁnite number of horizontal tangents. Find the
exact radian measure xcoordinatcs of these
horizontal, expressing the ﬁnal answer using
parameter n. Be sure to state whether your 11
represents all integers, all odd integers, all even integers, etc. i \
$(K) 2:“ H2.sz
Q Km’wZg‘mx _W ,ﬁﬁwwmsur» » {c'*F¢JTa‘.Z—ML"~“: m WW 8. Find each derivative: ﬁwﬁ:vlmﬁ.'rd,qaxapfﬁxhﬁ:vﬁ 4, ﬂy L MWMwi‘ﬁﬁtﬂ/WWN” >< vs
o“"” B. [:I Find the eguation of the tangent line to
the graph of y : cos"I x at x = 0 . Simpliﬁcation
is not required, but the y—coordinate of point of
tangency must be expressed in exact radian
measure form. owe a?) *‘ J
:a ._ 2 .. «L
3) y='(2l 1) Answe1 Q: Aim X?»
x dx
~
y: “Xmﬂjﬂs a. 1+ x  ‘t “‘3' X
X b) y=lr1(1+e‘”) H B
(A I 1 x < E “6‘” Q? ex. ‘ m ammmzwsaﬁwwwﬁw W
1» Pg? area Vmwmgwwwia ﬁrst Helix
iii: i‘i' e.“ H
... K" : “W gem j t 3:. er
“M” “33%. g e 1+ 9. Choose either A. or B. but not both. Check the box for ﬁle problem you want graded. A A. [:1 Find an eguation for the tangent line to the graph of 3c2 + xy — y2 : 4 at the point (2,2). equation: E: “a 2x+x¢§ﬂ+7~miy§izo
at \agwwm, a
*ﬁ”2‘/“ﬁw RY )2 X 2
y an 3x «a. [3% B. [3 Use logarithmic differentiation to ﬁnd 3% for y = x‘a’”. Express the ﬁnal answer explicitly as
a functlon of x. E g +6,“ K
%>/ :2. R X rhea”: ' {ﬁg
¥Ex3 _ {WK . 5;” +7, [ex , 593% 10. A movie camera is positioned 3000 feet from the base a rocket launch pad. Assume the rocket rises
vertically, and it’s speed is 600 ft/sec at the moment when the rocket has risen 4000 feet. How fast is the distance between the rocket and camera increasing at this moment? Express the ﬁnal answer using appropriate units. t d
aux/QM, \ Q it /
4L $3 {M'V‘C‘ 739L000 /
/
C
/ W "L at? i: i 7
300024 50000 '3: C: Answer: 3: $1180 iii/age
6 e3: EC) CD c3 11. Grain is dumped from a conveyor belt at a constant rate of 40 ﬁa/min . The grain forms a conical pile
whose heighLis alwaxi twice its radius. How fast is the radius of the pile increasing when the radius
is 5 feet? 1 For a cone, V = marrzh . Expr $3 the answer either in exact form or in decimal form rounded to the 3  3'” t . all! 2.
.__ I is Qwew gate/4W.” ...
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 Spring '11
 Teague
 Calculus

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